The quantum SU(3) invariant of links and Murasugi's congruence

Chbili, Nafaa

doi:10.1016/s0166-8641(01)00195-x

Cited by 7 publications

(22 citation statements)

References 10 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…As we have mentioned, we have corrected the false conjecture given by Chbili [4] and Przytycki and Sikora [30]. To compare with the ideal in [25], we observe that the ideal I n of Z[q ⌋ is a subset of the ideal generated by p and [2] p − [2] by the strong integrality of the quantum link invariant [21].…”

Section: Discussionmentioning

confidence: 88%

“…where A n is the ideal of Z[q For Conjecture 1.1, Chbili provided a proof for n = 3 using the representation theory of the quantum sl(3) [4]. There were subsequent studies on the conjecture [6].…”

Section: Conjecture 11 ([4]mentioning

confidence: 99%

“…Using the representation theory of complex simple Lie algebras, Reshetikhin and Turaev found quantized simple Lie algebras invariants of links and 3-manifolds [32,33] and these invariants have been studied extensively [4,5,13,28,16,27,45].…”

Section: Introductionmentioning

confidence: 99%

See 2 more Smart Citations

THE QUANTUM sl(n, ℂ) REPRESENTATION THEORY AND ITS APPLICATIONS

Jeong¹,

Kim²

2012

Journal of the Korean Mathematical Society

View full text Add to dashboard Cite

Abstract. In this paper, we study the quantum sl(n) representation category using the web space. Specially, we extend sl(n) web space for n ≥ 4 as generalized Temperley-Lieb algebras. As an application of our study, we find that the HOMFLY polynomial Pn(q) specialized to a one variable polynomial can be computed by a linear expansion with respect to a presentation of the quantum representation category of sl(n). Moreover, we correct the false conjecture [30] given by Chbili, which addresses the relation between some link polynomials of a periodic link and its factor link such as Alexander polynomial (n = 0) and Jones polynomial (n = 2) and prove the corrected conjecture not only for HOMFLY polynomial but also for the colored HOMFLY polynomial specialized to a one variable polynomial.

show abstract

Section: Discussionmentioning

confidence: 88%

Section: Conjecture 11 ([4]mentioning

confidence: 99%

See 1 more Smart Citation

THE QUANTUM sl(n, ℂ) REPRESENTATION THEORY AND ITS APPLICATIONS

Jeong¹,

Kim²

2012

Journal of the Korean Mathematical Society

View full text Add to dashboard Cite

show abstract

“…But one can easily see that the first and the last are , Figure 8. Normal chord diagrams of (4, 6, 8) and (6,6,6).…”

Section: Prime Cubic Bipartite Planar Graphsmentioning

confidence: 99%

“…For planar cubic bipartite graphs, some of symmetries can be orientation reversing. But the idea of the proof [6] still works in general with one exception. If the fundamental domain of the action is a basis web with the given boundary, then there does not exist any relation or expansion which can be applied repeatedly, thus Theorem 4.1 might not work.…”

Section: Prime Cubic Bipartite Planar Graphsmentioning

confidence: 99%

The Quantum 𝔰𝔩(3) Invariants of Cubic Bipartite Planar Graphs

Kim

Lee

2008

J. Knot Theory Ramifications

View full text Add to dashboard Cite

Temperley-Lieb algebras have been generalized to sl(3, C) web spaces. Since a cubic bipartite planar graph with suitable directions on edges is a web, the quantum sl (3) invariants naturally extend to all cubic bipartite planar graphs. First we completely classify them as a connected sum of primes webs. We also provide a method to find all prime webs and exhibit all prime webs up to 20 vertices. Using quantum sl(3) invariants, we provide a criterion which determine the symmetry of graphs.

show abstract

Quantum invariants and finite group actions on three-manifolds

Chbili

2004

Topology and its Applications

Self Cite

View full text Add to dashboard Cite

A 3-manifold M is said to be p-periodic (p ≥ 2 an integer) if and only if the finite cyclic group of order p acts on M with a circle as the set of fixed points. This paper provides a criterion for periodicity of rational homology three-spheres. Namely, we give a necessary condition for a rational homology three-sphere to be periodic with a prime period. This condition is given in terms of the quantum SU (3) invariant. We also discuss similar results for the Murakami-Ohtsuki-Okada invariant.

show abstract

The quantum SU(3) invariant of links and Murasugi's congruence

Cited by 7 publications

References 10 publications

THE QUANTUM sl(n, ℂ) REPRESENTATION THEORY AND ITS APPLICATIONS

THE QUANTUM sl(n, ℂ) REPRESENTATION THEORY AND ITS APPLICATIONS

The Quantum 𝔰𝔩(3) Invariants of Cubic Bipartite Planar Graphs

Quantum invariants and finite group actions on three-manifolds

Contact Info

Product

Resources

About